The chicken crossing the road joke, never got it and leave the damn chicken alone
It's an anti-joke. The joke is that you start off with something that sounds like it should be the setup to a joke, but then the punchline is 100% serious. The humor comes from the contrast between what you expect and what you get. You can find a whole compendium of other anti-jokes at places like anti-joke.com.
The Joke I don't understand is:
Boy, that's a lot of fish.
Sources tell me it's from a newer Godzilla title, and how it seemed to be a run-on sentence, but didn't seem to have anything after that phrase...
I certainly don't understand it. Does anybody else get the joke that may or may not exist within that black-hole of a sentence? Anybody?
That's yet another anti-joke. The context is that the army gets a huge pile of fish to lure out Godzilla, which surprises the main character when he sees just how much there is, and the camera zooms in on him like he's going to deliver some kind of clever fish-related one-liner, but instead he just makes the blatantly obvious observation that there are a lot of them. A lot of people also like to use it as evidence that the movie's writing is bad, though I personally think it's actually one of its more clever lines since they didn't go for the more obvious jokes.
Senpai jokes. I don't even know what a senpai is, sounds like a homoerotic massage.
"Senpai" is a Japanese honorific for a senior or upperclassman, like someone else said. It's a reference to a lot of low-quality highschool romcom anime where a common trope is younger girls getting crushes on their upperclassman but, rather than acting on them, just waiting passively for said upperclassman to "notice" them. This is a result of Japan's relatively conservative values system which discourages sexual and romantic aggression.
While it's not a bad trope on its own, especially since it
is something that happens often in the real world, it's so grossly overused in anime as a lazy writing crutch that it's become an inside joke in the otaku community.
I never got the phrase inb4. Shotte tried explaining (though vaguely) once but I know nothing of it. It might not even be a joke for all I know.
It literally means "in before" but is usually used more like "I predict" or "I'm calling this". It just means you're getting your prediction
in before the thing actually comes to pass.